2016/6/23Election Algorithms1 Introduction to Distributed Algorithm Part Two: Fundamental Algorithm Chapter 7- Election Algorithms Teacher: Chun-Yuan Lin

2016/6/23Election Algorithms2 Election Algorithms (1) In this chapter the problem of election, also called leader finding, will be discussed. The election problem was first posed by LeLann (Subsection ). The problem is to start from a configuration where all processes are in the same state, and arrive at a configuration where exactly one process is in state leader and all other processes are in the state lost. An election under the processes must be held if a centralized algorithm is to be executed and there is no a priori candidate to serve as the initiator of this algorithm.

2016/6/23Election Algorithms3 Election Algorithms (2) A large number of results about the election problem exist.

2016/6/23Election Algorithms4 Introduction (1) The process in state leader at the end of the computation is called the leader and is said to be elected by the algorithm.

2016/6/23Election Algorithms5 Introduction (2)

2016/6/23Election Algorithms6 Assumptions Made in this Chapter (1) The election problem has been studied in this chapter under assumptions that we now review

2016/6/23Election Algorithms7 Assumptions Made in this Chapter (2)

2016/6/23Election Algorithms8 Elections and Waves Election with the tree algorithm (find smallest identity) Election with the phase algorithm Election with Finn's algorithm

2016/6/23Election Algorithms9 (leave to root) (root to leave)

2016/6/23Election Algorithms10 Ring Networks (1) In this section some election algorithms for unidirectional rings are considered. The election problem was first posed for the context of ring networks by LeLann (message complexity O(N 2 ) ). This solution was improved by Chang and Roberts (worst case complexity O(N 2 ), average case complexity O(NlogN)). Hirschberg-Sinclair algorithm required channels to be bidirectional (worst case complexity O(NlogN)).

2016/6/23Election Algorithms11 Ring Networks (2) Petersen and Dolev, Klawe, and Rodeh independently proposed all O(NlogN) solution for the unidirectional ring. A worst case lower bound of 0.34N log N messages for bidirectional rings was proved by Bodlaender. Pachl, Korach, and Rotem proved lower bounds of Ω(NlogN) for the average case complexity, both for bidirectional and unidirectional rings.

2016/6/23Election Algorithms12 The Algorithms of LeLann and of Chang and Roberts (1) The Algorithms of LeLann unidirectional rings (more than one initiator) (some are not initiator) (receive all tok)

2016/6/23Election Algorithms13 The Algorithms of LeLann and of Chang and Roberts (2) The Algorithms of Chang and Roberts

2016/6/23Election Algorithms14 unidirectional rings (only pass better tok)

2016/6/23Election Algorithms15 The Peterson/Dolev-Klawe-Rodeh Algorithm

2016/6/23Election Algorithms16 unidirectional rings (until only one active) (not, send again)

2016/6/23Election Algorithms17 A Lower-bound Result (1) The result is due to Pachl, Korach, and Rotem and is obtained under the following assumptions.

2016/6/23Election Algorithms18 A Lower-bound Result (2)

2016/6/23Election Algorithms19 Arbitrary Networks

2016/6/23Election Algorithms20 Extinction and a Fast Algorithm (1)

2016/6/23Election Algorithms21 Extinction and a Fast Algorithm (2) (only one wave)

2016/6/23Election Algorithms22 The Gallager-Humblet-Spira Algorithm (1)

2016/6/23Election Algorithms23 The Gallager-Humblet-Spira Algorithm (2)

2016/6/23Election Algorithms24 Global Description of the GHS Algorithm (1)

2016/6/23Election Algorithms25 Global Description of the GHS Algorithm (2)

2016/6/23Election Algorithms26 Global Description of the GHS Algorithm (3)

2016/6/23Election Algorithms27 Detailed Description of the GHS Algorithm (1)

2016/6/23Election Algorithms28 Detailed Description of the GHS Algorithm (2)

2016/6/23Election Algorithms29 Detailed Description of the GHS Algorithm (3)

2016/6/23Election Algorithms30 The Korach-Kutten-Nloran Algorithm

2016/6/23Election Algorithms31

2016/6/23Election Algorithms32 Applications of the KKM Algorithm